how to smooth the eyelid?
It depends on your mesh. If the eyesockets are UV spheres with the poles left and right then it's fairly easy.
You might need one or two more edge loops that work as the compressed lids. To close the lids you rotate the edge loops over the eyeball, the upper lid down and the bottom lid up.

You can do this in the following way:

Select the vertices of the upper lid and assign them to a vertice group Ctrl + G. That way you can easily select them again.

Clear selection Alt + H and select the vert at the pole. Then you can move the 3D Cursor to this postion (Shift + S).

Choose 3D Cursor as the Transformation Pivot Point (see (1) on the image).

the eyes of your model are tilted in space so the front or side view won't work. But you can adjust the view with Shift + Numpad 7 to the pole vertice (or use menu View → Align View → Align View to Active → Top).

Finally, clear selection Alt + H and select the vertice group of the upper lid Ctrl + G. Then rotate these vertices along the eyeball (R). Check the vertices on the other side. You can adjust the position or rotate them individually if needed.



Repeat the steps for the lower eyelid. With a Solidify modifier you can add easily depth to the eyelids. Save the deformation in Shape Keys and animate it. Hope that helps.